Problem: The grades on a physics midterm at Springer are normally distributed with $\mu = 75$ and $\sigma = 4.5$. Ishaan earned a $64$ on the exam. Find the z-score for Ishaan's exam grade. Round to two decimal places.
A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Ishaan's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{64 - {75}}{{4.5}}} $ ${ z \approx -2.44}$ The z-score is $-2.44$. In other words, Ishaan's score was $2.44$ standard deviations below the mean.